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Dissipation-Shaped Quantum Geometry in Nonlinear Transport.

Zhichao Guo¹, Xing-Yuan Liu¹, Hua Wang¹

¹Zhejiang University, Center for Quantum Matter, School of Physics, Hangzhou 310058, China.

Physical Review Letters

|June 7, 2026

Summary

This summary is machine-generated.

The intrinsic nonlinear Hall effect

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Area of Science:

Condensed matter physics
Quantum geometry
Quantum transport

Background:

The intrinsic nonlinear Hall effect is crucial for understanding quantum geometry.
Existing theories present conflicting expressions for dissipation-independent conductivity.
This ambiguity hinders a universal understanding of the phenomenon.

Purpose of the Study:

To resolve ambiguities in the theory of the intrinsic nonlinear Hall effect.
To clarify the dependence of the nonlinear Hall conductivity on dissipation mechanisms.
To establish a benchmark for the exact calculation of this conductivity.

Main Methods:

Solving the exact nonequilibrium steady state (NESS) density matrix for a generic Bloch system.
Coupling the system to a featureless fermionic bath.
Analyzing the decomposition of the conductivity into geometric and kinetic parts.

Main Results:

The intrinsic nonlinear Hall conductivity is not universal and depends on the dissipation mechanism.
The exact conductivity decomposes into a geometric part (σgeo) and a novel kinetic part (σkin).
The geometric part clarifies inconsistencies related to the quantum metric, while the kinetic part arises from modified occupation functions.

Conclusions:

The nonlinear Hall conductivity is contingent on the physical system-bath coupling, not solely the Bloch Hamiltonian.
Dissipation mechanisms uniquely shape the NESS density matrix, influencing the conductivity.
This work provides a definitive framework for understanding intrinsic nonlinear Hall conductivity.